Entanglement measures under symmetry - art. no. 062307

We show how to simplify the computation of the entanglement of formation an d the relative entropy of entanglement for states, which are invariant unde r a group of local symmetries. For several examples of groups we characteri ze the state spaces, which are invariant under these groups. For specific e xamples we calculate the entanglement measures. In particular, we derive an explicit formula for the entanglement of formation for (U x U)-invariant s tates, and we find a counterexample of the additivity conjecture for the re lative entropy of entanglement.